FA-65251 / Epidemic compartment models / Open access
Delay-adjusted case fatality ratio: pmf lag origin · case 01
Every delay is shifted by one day, understating resolved cases.
ROOT CAUSE
The pmf index is treated as starting at lag 1.
VERIFIED REPAIR
Restore the pmf lag origin rule: `enumerate(delay_pmf)`.
Unsuccessful approach: Dropping the lag-0 mass loses same-day deaths.
Case contract
naive CFR = sum(deaths)/sum(cases); delay_pmf[j] is the probability that death occurs j days after onset (j from 0); known = sum_t sum_j cases[t-j]*pmf[j] over t in the series; adjusted = min(sum(deaths)/known, 1); return [naive rounded 6, adjusted rounded 6 or None when known is 0]; None when there are no cases.
Why this case matters
Compartmental epidemic calculations drive outbreak forecasts, vaccine targets and hospital planning; a single wrong flow, rate conversion or boundary silently changes every downstream number.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cases, deaths, delay_pmf):
total_cases = sum(cases)
total_deaths = sum(deaths)
if total_cases <= 0:
return None
naive = total_deaths / total_cases
known = 0.0
for t in range(len(cases)):
for j, f in enumerate(delay_pmf, 1):
if t - j >= 0:
known += cases[t - j] * f
if known <= 0:
return [round(naive, 6), None]
adjusted = min(total_deaths / known, 1.0)
return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: growing epidemic | [0.025806, 0.16] | [0.025806, 0.072727] | Failed |
| regression: stable epidemic | [0.03, 0.046154] | [0.03, 0.036735] | Failed |
| control: long delay no outcomes | [0.0, None] | [0.0, None] | Passed |
| control: no cases | None | None | Passed |
| regression: adjusted exceeds one | [0.076923, None] | [0.076923, 1.0] | Failed |
| regression: immediate deaths | [0.093333, 0.14] | [0.093333, 0.093333] | Failed |
| regression: single day | [0.025, None] | [0.025, 0.041667] | Failed |
SHA-256 / dc530a1f35ed8fbd088fef29f97fdcc6ddb36ac3abf9228ea1d5ef42c62ffc86
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cases, deaths, delay_pmf):
total_cases = sum(cases)
total_deaths = sum(deaths)
if total_cases <= 0:
return None
naive = total_deaths / total_cases
known = 0.0
for t in range(len(cases)):
for j, f in enumerate(delay_pmf[1:]):
if t - j >= 0:
known += cases[t - j] * f
if known <= 0:
return [round(naive, 6), None]
adjusted = min(total_deaths / known, 1.0)
return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: growing epidemic | [0.025806, 0.047904] | [0.025806, 0.072727] | Failed |
| regression: stable epidemic | [0.03, 0.04] | [0.03, 0.036735] | Failed |
| control: long delay no outcomes | [0.0, None] | [0.0, None] | Passed |
| control: no cases | None | None | Passed |
| regression: adjusted exceeds one | [0.076923, 1.0] | [0.076923, 1.0] | Passed |
| regression: immediate deaths | [0.093333, None] | [0.093333, 0.093333] | Failed |
| regression: single day | [0.025, 0.0625] | [0.025, 0.041667] | Failed |
SHA-256 / 7c1fcd20187d33abe91c7ef4e7b1a080b479bbf20050b91f81b3305bedbfb743
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(cases, deaths, delay_pmf):
total_cases = sum(cases)
total_deaths = sum(deaths)
if total_cases <= 0:
return None
naive = total_deaths / total_cases
known = 0.0
for t in range(len(cases)):
for j, f in enumerate(delay_pmf):
if t - j >= 0:
known += cases[t - j] * f
if known <= 0:
return [round(naive, 6), None]
adjusted = min(total_deaths / known, 1.0)
return [round(naive, 6), round(adjusted, 6)]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: stable epidemic',
([50, 50, 50, 50, 50, 50], [0, 1, 2, 2, 2, 2], [0.2, 0.5, 0.3]),
[0.03, 0.036735]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])],
[('regression: growing epidemic',
([10, 20, 40, 80, 160], [0, 0, 1, 2, 5], [0.1, 0.3, 0.4, 0.2]),
[0.025806, 0.072727]),
('control: long delay no outcomes', ([5, 8, 12], [0, 0, 0], [0, 0, 0, 0, 0, 1]), [0.0, None]),
('control: no cases', ([0, 0, 0], [0, 0, 0], [0.5, 0.5]), None),
('regression: adjusted exceeds one', ([1, 1, 50], [1, 1, 2], [0.0, 0.0, 1.0]), [0.076923, 1.0]),
('regression: immediate deaths', ([20, 30, 25], [2, 3, 2], [1.0]), [0.093333, 0.093333]),
('regression: single day', ([40], [1], [0.6, 0.4]), [0.025, 0.041667]),
('regression: late surge',
([5, 5, 5, 60, 90], [0, 0, 1, 1, 2], [0.05, 0.25, 0.4, 0.3]),
[0.024242, 0.111111])]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: growing epidemic | [0.025806, 0.072727] | [0.025806, 0.072727] | Passed |
| regression: stable epidemic | [0.03, 0.036735] | [0.03, 0.036735] | Passed |
| control: long delay no outcomes | [0.0, None] | [0.0, None] | Passed |
| control: no cases | None | None | Passed |
| regression: adjusted exceeds one | [0.076923, 1.0] | [0.076923, 1.0] | Passed |
| regression: immediate deaths | [0.093333, 0.093333] | [0.093333, 0.093333] | Passed |
| regression: single day | [0.025, 0.041667] | [0.025, 0.041667] | Passed |
SHA-256 / 01ee2c9d630e6727e1687eea9652a6ffb68915f863ebe60f5a37a8cf8474002c
Verification & scope
Deterministic bounded teaching model with a stipulated contract; not a validated scientific or public-health modelling library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:47:32.072150+00:00.
Case digest / 78ccea63187956d76a97393b2f0ee739b36158355a4e09347527c319bb3a5e9d